legendre_rule, a C code which generates a specific Gauss-Legendre quadrature rule, based on user input.
The rule is written to three files for easy use as input to other programs.
The Gauss-Legendre quadrature rule is used as follows:
Integral ( A <= x <= B ) f(x) dx
is to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
legendre_rule order a b filenamewhere
The computer code and data files described and made available on this web page are distributed under the MIT license
legendre_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
CCN_RULE, a C code which defines one of a set of nested Clenshaw Curtis quadrature rules.
CLENSHAW_CURTIS_RULE, a C code which defines a Clenshaw Curtis quadrature rule.
HERMITE_RULE, a C code which can compute and print a Gauss-Hermite quadrature rule.
LAGUERRE_RULE, a C code which can compute and print a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).
LEGENDRE_EXACTNESS, a C code which tests the monomial exactness of quadrature rules for the Legendre problem of integrating a function with density 1 over the interval [-1,+1].
LEGENDRE_POLYNOMIAL, a C code which evaluates the Legendre polynomial and associated functions.
LEGENDRE_RULE_FAST, a C code which uses a fast (order N) algorithm to compute a Gauss-Legendre quadrature rule of given order.
LINE_FELIPPA_RULE, a C code which returns the points and weights of a Felippa quadrature rule over the interior of a line segment in 1D.
LINE_NCC_RULE, a C code which computes a Newton Cotes Closed (NCC) quadrature rule for the line, that is, for an interval of the form [A,B], using equally spaced points which include the endpoints.
LINE_NCO_RULE, a C code which computes a Newton Cotes Open (NCO) quadrature rule, using equally spaced points, over the interior of a line segment in 1D.
PATTERSON_RULE, a C code which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
QUADRATURE_RULES_LEGENDRE, a dataset directory which contains triples of files defining standard Gauss-Legendre quadrature rules.
QUADRULE, a C code which defines 1-dimensional quadrature rules.
TRUNCATED_NORMAL_RULE, a C code which computes a quadrature rule for a normal probability density function (PDF), also called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].